feat: add Difference Array algorithm implementation and tests (#7244)

src/main/java/com/thealgorithms/prefixsum/DifferenceArray.java

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+package com.thealgorithms.prefixsum;
+
+/**
+ * Implements the Difference Array algorithm.
+ *
+ * <p>
+ * The Difference Array is an auxiliary data structure that enables efficient range update operations.
+ * It is based on the mathematical concept of Finite Differences.
+ * </p>
+ *
+ * <p>
+ * <strong>Key Operations:</strong>
+ * <ul>
+ * <li>Range Update (Add value to [L, R]): O(1)</li>
+ * <li>Reconstruction (Prefix Sum): O(N)</li>
+ * </ul>
+ * </p>
+ *
+ * @see <a href="https://en.wikipedia.org/wiki/Finite_difference">Finite Difference (Wikipedia)</a>
+ * @see <a href="https://en.wikipedia.org/wiki/Prefix_sum">Prefix Sum (Wikipedia)</a>
+ * @author Chahat Sandhu, <a href="https://github.com/singhc7">singhc7</a>
+ */
+public class DifferenceArray {
+
+    private final long[] differenceArray;
+    private final int n;
+
+    /**
+     * Initializes the Difference Array from a given integer array.
+     *
+     * @param inputArray The initial array. Cannot be null or empty.
+     * @throws IllegalArgumentException if the input array is null or empty.
+     */
+    public DifferenceArray(int[] inputArray) {
+        if (inputArray == null || inputArray.length == 0) {
+            throw new IllegalArgumentException("Input array cannot be null or empty.");
+        }
+        this.n = inputArray.length;
+        // Size n + 1 allows for branchless updates at the right boundary (r + 1).
+        this.differenceArray = new long[n + 1];
+        initializeDifferenceArray(inputArray);
+    }
+
+    private void initializeDifferenceArray(int[] inputArray) {
+        differenceArray[0] = inputArray[0];
+        for (int i = 1; i < n; i++) {
+            differenceArray[i] = inputArray[i] - inputArray[i - 1];
+        }
+    }
+
+    /**
+     * Adds a value to all elements in the range [l, r].
+     *
+     * <p>
+     * This method uses a branchless approach by allocating an extra element at the end
+     * of the array, avoiding the conditional check for the right boundary.
+     * </p>
+     *
+     * @param l   The starting index (inclusive).
+     * @param r   The ending index (inclusive).
+     * @param val The value to add.
+     * @throws IllegalArgumentException if the range is invalid.
+     */
+    public void update(int l, int r, int val) {
+        if (l < 0 || r >= n || l > r) {
+            throw new IllegalArgumentException(String.format("Invalid range: [%d, %d] for array of size %d", l, r, n));
+        }
+
+        differenceArray[l] += val;
+        differenceArray[r + 1] -= val;
+    }
+
+    /**
+     * Reconstructs the final array using prefix sums.
+     *
+     * @return The resulting array after all updates. Returns long[] to handle potential overflows.
+     */
+    public long[] getResultArray() {
+        long[] result = new long[n];
+        result[0] = differenceArray[0];
+
+        for (int i = 1; i < n; i++) {
+            result[i] = differenceArray[i] + result[i - 1];
+        }
+        return result;
+    }
+}

src/test/java/com/thealgorithms/prefixsum/DifferenceArrayTest.java

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+package com.thealgorithms.prefixsum;
+
+import static org.junit.jupiter.api.Assertions.assertArrayEquals;
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertThrows;
+
+import org.junit.jupiter.api.Test;
+
+class DifferenceArrayTest {
+
+    @Test
+    void testStandardRangeUpdate() {
+        int[] input = {10, 20, 30, 40, 50};
+        DifferenceArray da = new DifferenceArray(input);
+
+        da.update(1, 3, 5);
+
+        long[] expected = {10, 25, 35, 45, 50};
+        assertArrayEquals(expected, da.getResultArray());
+    }
+
+    @Test
+    void testMultipleOverlappingUpdates() {
+        int[] input = {10, 10, 10, 10, 10};
+        DifferenceArray da = new DifferenceArray(input);
+
+        da.update(0, 2, 10);
+        da.update(2, 4, 20);
+
+        long[] expected = {20, 20, 40, 30, 30};
+        assertArrayEquals(expected, da.getResultArray());
+    }
+
+    @Test
+    void testIntegerOverflowSafety() {
+        int[] input = {Integer.MAX_VALUE, 100};
+        DifferenceArray da = new DifferenceArray(input);
+
+        da.update(0, 0, 100);
+
+        long[] result = da.getResultArray();
+        long expectedVal = (long) Integer.MAX_VALUE + 100;
+
+        assertEquals(expectedVal, result[0]);
+    }
+
+    @Test
+    void testFullRangeUpdate() {
+        int[] input = {1, 2, 3};
+        DifferenceArray da = new DifferenceArray(input);
+
+        da.update(0, 2, 100);
+
+        long[] expected = {101, 102, 103};
+        assertArrayEquals(expected, da.getResultArray());
+    }
+
+    @Test
+    void testBoundaryWriteOptimization() {
+        int[] input = {5, 5};
+        DifferenceArray da = new DifferenceArray(input);
+
+        da.update(1, 1, 5);
+
+        long[] expected = {5, 10};
+
+        assertArrayEquals(expected, da.getResultArray());
+    }
+
+    @Test
+    void testLargeMassiveUpdate() {
+        int[] input = {0};
+        DifferenceArray da = new DifferenceArray(input);
+
+        int iterations = 100000;
+        for (int i = 0; i < iterations; i++) {
+            da.update(0, 0, 1);
+        }
+
+        assertEquals(100000L, da.getResultArray()[0]);
+    }
+
+    @Test
+    void testNullInputThrowsException() {
+        assertThrows(IllegalArgumentException.class, () -> new DifferenceArray(null));
+    }
+
+    @Test
+    void testEmptyInputThrowsException() {
+        assertThrows(IllegalArgumentException.class, () -> new DifferenceArray(new int[] {}));
+    }
+
+    @Test
+    void testInvalidRangeNegativeIndex() {
+        DifferenceArray da = new DifferenceArray(new int[] {1, 2, 3});
+        assertThrows(IllegalArgumentException.class, () -> da.update(-1, 1, 5));
+    }
+
+    @Test
+    void testInvalidRangeOutOfBounds() {
+        DifferenceArray da = new DifferenceArray(new int[] {1, 2, 3});
+        assertThrows(IllegalArgumentException.class, () -> da.update(0, 3, 5));
+    }
+
+    @Test
+    void testInvalidRangeStartGreaterThanEnd() {
+        DifferenceArray da = new DifferenceArray(new int[] {1, 2, 3});
+        assertThrows(IllegalArgumentException.class, () -> da.update(2, 1, 5));
+    }
+}